He pleaded for a two-month period of "reflection" as he apologised for his role in an internal church probe into notorious sex offender Fr Brendan Smyth and admitted he had failed victims.
The Primate of All Ireland was speaking ahead of the Pope's long-awaited pastoral letter dealing with the litany of clerical sex abuse scandals in Ireland, which he will sign tomorrow.
The Lenten Letter, the first papal document devoted exclusively to paedophilia, follows the damning Murphy report on widespread child abuse by priests in the Dublin archdiocese.
Speaking in English to pilgrims and tourists in St Peter's Square, the Vatican, Pope Benedict said he hoped the letter would "help in the process of repentance, healing and renewal".
"The church in Ireland has been severely shaken as a result of the child abuse crisis. As a sign of my deep concern, I have written a pastoral letter dealing with this painful situation. I ask all of you to read it for yourselves, with an open heart and in a spirit of faith," the Pope added.
In an emotional St Patrick's Day homily in Armagh, Cardinal Brady said he would "consider my position" as he came under mounting pressure to resign.
Crucially, his period of reflection to seek "the guidance of the Holy Spirit" will cover not only Holy Week and Easter but also extend to Pentecost, a major date in the liturgical calendar that comes 48 to 50 days after Easter.
It falls on Sunday, May 23, buying the cardinal two months as he battles for survival.
A further easing of the cardinal's position came after Smyth's religious order, the Norbertine Community, broke its silence on the controversy.
In a statement, the order apologised for not being able to control the serial paedophile, who was sent several times for psychiatric treatment.
It admitted the only way to have dealt with Smyth was to have him jailed under the criminal law system.
However, victims' groups last night reacted with disappointment after Cardinal Brady indicated he had no immediate plans to resign.
Marie Collins, a victim of clerical abuse in Dublin, urged him to "do the honourable thing and step down".
Sam Adair, who was abused by Smyth as a boy, added: "He (Cardinal Brady) has no grounds for remaining. He has no credibility, this had to be dragged from the church. It's hideous to think he silenced two children who were being abused."
One of Smyth's victims -- named only as 'Samantha' -- again questioned the cardinal's position. 'Samantha' said the cardinal must answer whether his inaction led to her being raped and abused.
The North's Deputy First Minister Martin McGuinness earlier became the most senior politician to openly call for Cardinal Brady's resignation.
Speaking in Washington, Mr McGuinness said: "I think many Catholics will be dismayed at the news that they are hearing almost on a daily basis. I do think Cardinal Brady needs to consider his position."
Fr Stephen Kearney, a priest in Newtownstewart, Co Tyrone, criticised Mr McGuinness's intervention, which he said was "clouding the water".
Meanwhile, the Catholic Communications Office insisted Cardinal Brady was not present during a third investigation into Smyth in 1975.
It was originally believed the cardinal had been present during interviews with two child victims, a boy and a girl.
The girl, who told members of the clergy that Smyth had abused her during outings from 1970 to 1975, later brought a civil case against the Catholic Church in 1997 and against Cardinal Brady as its head.
In a statement, the Catholic Communications Office gave details of two meetings at which he was present. It insisted both of these were with teenage boys.
The first meeting took place in Dundalk, Co Louth, on March 29, 1975, and involved a 14-year-old boy. The second took place at the Parochial House in Ballyjamesduff, Co Cavan, on April 4, 1975, and was with a 15-year-old boy.
A spokesman insisted the cardinal was only present during these two interviews and was not involved in any interview with a girl.
At the first meeting, Cardinal Brady, then a 36-year-old priest, was joined by two other priests. His role was to take notes. At the second, he was alone with the child and was responsible for conducting the inquiry and taking notes.
The spokesman claimed the decision to ask the children to sign an oath of secrecy was to "avoid potential collusion in the gathering of the inquiry's evidence and to ensure that the process was robust enough to withstand challenge by the perpetrator, Fr Brendan Smyth".